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This paper presents mean-square analysis for the transform domain least mean-square (LMS) adaptive algorithm with a new time-varying step size control method. The variable step size approximates a theoretical optimal one based on the minimization of the mean weighted squared norm of the coefficient error vector. This cost function represents a direct measure of the distance between the adaptive filter coefficients and the optimum solution, therefore leading to significant improvements in the performance properties of the TDLMS algorithm. An expression for the steady state excess mean-square error (MSE) is derived, which shows that the input signal statistics and the adaptive filter length have a marginal effect on the steady state performance of the proposed algorithm. The theoretical steady state results are verified by simulation experiments.